Saturday, 2 February 2013

Probability for wargamers 8 - +1 vs reroll

It's one of the rule-writers' common ways of making weapons in Warhammer-like d6 systems different. Some weapons get +1 to hit, some get a reroll. Which is better though?

Interesting question, and with the amount of stuff we've worked out in previous posts, not that hard.

With a target number of four, for example:

Your normal odds are 3 in 6, or 50%.

With a +1, obviously, they become 4 in 6, or 66.7%.

For the reroll, you have a 50% chance of succeeding on the first attempt, plus odds of (chance to miss * chance to hit a second time), i.e. 50% + (50% of 50%). Which makes 75%. Clearly the reroll's the better bet.

I won't work out the details for other target numbers: here's the table:

Normal

+1 to hit

Re-roll misses

3

66.67%

83.33%

88.89%

4

50.00%

66.67%

75.00%

5

33.33%

50.00%

55.56%

6

16.67%

33.33%

30.56%

OK, so it looks like the re-roll's a better bet unless your target is hard to hit.

Another favourite of designers is the '+1 strength' modifier on the wound roll. Let's look at that: typically, for WAB, equal STR means wounding on a 4.

Hit+Wound (normal)

Hit+Wound (norm/+1STR)

Hit+Wound (reroll)

3

33.33%

44.44%

44.44%

4

25.00%

33.33%

37.50%

5

16.67%

22.22%

27.78%

6

8.33%

11.11%

15.28%

Again, interesting, The re-roll's still better, but less so.

Moral of the story? Given the choice? Take the weapon that gives the re-roll!